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Lecture

# GGR270 Lecture #5 Oct. 10 2012.pdf

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School
University of Toronto St. George
Department
Geography
Course
GGR270H1
Professor
Damian Dupuy
Semester
Fall

Description
GGR270  Lecture  #5       October  10,  2012     Probability  (continued)   • Focuses  on  the  occurrence  of  an  event   o Where  one  of  several  possible  outcomes  could  result.   o Outcomes  are  and  must  be  mutually  exclusive;  is  either  /  or.   • Can  be  thought  of  as  a  frequency  of  an  event  occurring  relative  to  other   outcomes.   • P(A)  =  F(A)  /  F(E)  where:   o P(A)  –  probability  of  outcome  A  occurring   o F(A)  –  absolute  frequency  of  A   o F(E)  –  frequency  of  all  outcomes   • Example  1:   o Die  has  6  faces  numbers  1-­‐6   o What  is  the  likelihood  of  throwing  a  6  in  one  throw?   o P(6)  =  1/6  or  1  in  6  or  .167   o Same  probability  exists  for  each  of  those  outcomes  too.   • Example  2:   o Examine  the  record  of  wet  and  dry  days  over  a  100  day  period.   o 62  days  recorded  as  dry.   o 38  days  recorded  as  wet.   o What  is  the  probability  of  a  wet  day  occurring?   o P(wet)  =  #  of  wet  days/total  #  of  days  =  38/100  =  .38  or  38%   o Alternatively,  probability  of  a  dry  day  occurring  is     o P(dry)  =  62/100  =  .62  or  62%     Probability  Rules   • Maximum  probability  of  an  outcome  is  1.0   o All  probability  must  add  up  to  one  or  0.0≤P(A)≤1.0.   o Probability  will  lie  between  zero  and  1.   • Addition  rule:   o Used  when  finding  probability  of  single  independent  events.   o What’s  the  probability  of  two  or  more  events  occurring  that  have  no   relationship  to  one  another.     o Used  whenever  you  see  ‘or’.   o P(A  or  B)  =  P(A)  +  P(B)   o Example:    What  is  the  probability  of  throwing  a  6  or  5  in  a  single  throw?    P(6)  =  .167    P(5)  =  .167    Therefore  probability  of  throwing  a  5  or  6  =  P(6)  +  P(5)  or   .167  +  .167  =  .334   • Multiplication  rule:   o Used  when  finding  probability  of  multiple  independent  events.   o Now  specifying  the  same  order   o Can  be  two  or  more  events  occurring  together.   o Used  when  you  see  ‘and’.     1   GGR270  Lecture  #5       October  10,  2012     o P(A  and  B)  =  P(A)  ×  P(B)   o Example:    What  is  the  probability  of  rolling  two  sixes  in  subsequent   throws?
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